Goodlife Fitness vs. L.A Fitness

Graphing Linear Relations

Introductory Statement

Goodlife fitness and L.A fitness are both fitness centers and offer yearly memberships. Goodlife fitness offers a yearly membership for $350 plus $4 per visit, whereas L.A fitness offers a yearly membership for $400 plus $2 per visit.

Goodlife Fitness

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L.A Fitness

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Equation for Goodlife Fitness

Goodlife Fitness

y=mx+b

C= 4v+350

C= Total Cost

V= # of visits

Slope=m

Slope=4

Equation for L.A Fitness

L.A Fitness

y=mx+b

C=2v+400

C= Total Cost

V= # of visits

Slope=m

Slope=2

The Graph

Total Cost ($) Vs. Number of Visits
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Blue Line- L.A Fitness

Red Line- Goodlife Fitness

y-axis: Total Cost ($)

x-axis: # of Visits

(applies to graph below and above)

Y-intercepts of both Lines

Total Cost ($) Vs. Number of Visits
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The y-intercepts show that the initial cost of a membership at Goodlife Fitness is $350 and the initial cost of a membership at L.A Fitness is $400.

The Point of Intersection/ Solution

The point of intersection on the graph, is basically where the two lines meet. On this graph the point of intersection is (25,450), this means that if you visit either fitness center 25 times in the whole year the cost will be the same for both memberships which would be $450 in total. Also, you should plan ahead of how many times you are planning to go to the fitness center because if you are planning to go less than 25 times in the year Goodlife fitness is a cheaper option, whereas if you are planning to go more than 25 times in the year L.A Fitness is a cheaper option. This is shown in the graph and the table, as in the table you can clearly see that the total cost for membership up till 25 visits is less for Goodlife Fitness than L.A Fitness, also in the table you can see that the total cost for membership after 25 visits is less for L.A Fitness than Goodlife Fitness. In the graph you can see that the line that represents Goodlife Fitness has a lower y-intercept than the line that represents L.A Fitness, which means that that the values for Goodlife Fitness would be less than the values for L.A Fitness until the point of intersection, and after the point of intersection since the slope of the red line (Goodlife Fitness) is higher than the blue line (L.A Fitness), the values for Goodlife Fitness turn out to be higher than L.A Fitness after the point of intersection.

Summary Statement

The cost of both memberships from Goodlife fitness and L.A fitness will be $450 in total if you visit the fitness center 25 times during the year.